New extended superconformal sigma models and Quaternion Kahler manifolds

Abstract

Quaternion Kahler manifolds are known to be the target spaces for matter hypermultiplets coupled to N=2 supergravity. It is also known that there is a one-to-one correspondence between 4n-dimensional quaternion Kahler manifolds and those 4(n+1)-dimensional hyperkahler spaces which are the target spaces for rigid superconformal hypermultiplets (such spaces are called hyperkahler cones). In this paper we present a projective-superspace construction to generate a hyperkahler cone M^{4(n+1)}_H of dimension 4(n+1) from a 2n-dimensional real analytic Kahler-Hodge manifold M^{2n}_K. The latter emerges as a maximal Kahler submanifold of the 4n-dimensional quaternion Kahler space M^{4n}_Q such that its Swann bundle coincides with M^{4(n+1)}_H. Our approach should be useful for the explicit construction of new quaternion Kahler metrics. The results obtained are also of interest, e.g., in the context of supergravity reduction N=2 --> N=1, or alternatively from the point of view of embedding N=1 matter-coupled supergravity into an N=2 theory.

30 pages

References in corpus (9)

• String loop corrected hypermultiplet moduli spaces
• 4D N = 2 Supergravity and Projective Superspace
• On conformal supergravity and projective superspace
• On superconformal projective hypermultiplets
• On N = 2 supergravity and projective superspace: Dual formulations
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics
• Chiral formulation for hyperkaehler sigma-models on cotangent bundles of symmetric spaces
• A note on conformal symmetry in projective superspace

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